Before I give my suggestions for cigars, I recommend this. Go to your local cigar store see what they have to offer and if the they will help out. They should be more than accommodating. If not, here's what I would do. First go with a larger cigar, maybe a churchill or torpedo. You don't have to finish it, so don't force yourself. But a cigar that size should stay a little cooler. That way the heat won't get to your throat as fast. After that try a Dominican cigar. They are generally (I use this loosely) less spicy than, say, Nicaraguan. Maybe a partagas 'S' series, that should be good. Lastly, if you are outside the US, you can go cuban. If so, try a H.upman Connaisseur No.1. They are flavorful but mild.

But I would first go to a local shop and see what they offer.